The Group and Hamiltonian Descriptions of Hydrodynamical Systems

DOI10.1007/978-3-642-00837-5_4zbMath1305.76025OpenAlexW956454786MaRDI QIDQ5171890

Boris A. Khesin

Publication date: 12 February 2015

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-00837-5_4

Mathematics Subject Classification ID

Hamilton's equations (70H05) Soliton equations (35Q51) Applications of manifolds of mappings to the sciences (58D30) Incompressible inviscid fluids (76B99) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65)

Cites Work

• Korteweg - de Vries suoerequation as an Euler equation
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Topological methods in hydrodynamics
• Euler equations on homogeneous spaces and Virasoro orbits
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Hydrodynamical description of the continuous Heisenberg chain
• The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex filament dynamics
• The Geometry of Infinite-Dimensional Groups
• The degree of knottedness of tangled vortex lines
• A soliton on a vortex filament
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